Measurement errors from instruments are often modeled using the uniform distribution to determine the range of large public address system, acoustical engineers use a method of triangulation to measure the shock waves sent out by the speakers. The time at which the waves arrive at the sensors must be measured accurately. In this context, a negative error means the signal arrived too early. A positive error means the signal arrived too late. Measurement errors in reading these times have a uniform distribution from -0.05 to +0.05 microseconds. (Reference: J. Perruzi and E. Hilliard, "Modeling Time Delay Measurements Errors,"Journal of the Acoustical Society of America, Vol. 75, No. 1, pp. 197 - 201.)

What is the probability that such measurements will be in error by

(a) less than +0.03 microsecond (i.e., -0.05x <0.03

)?

(Round to four decimal places.)

(b) more than -0.02 microsecond?

(Round to four decimal places.)

(c) between -0.04 and +0.01 microsecond?

(Round to four decimal places.)

(d) Find the mean and standard deviation of measurement errors.(Round to four decimal places.)

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Measurements from an instrument are calledunbiasedif the mean of the measurement errors is zero. Would you say the measurements for these acoustical sensors are unbiased?